Maximal inequalities and Riesz transforms for vector-valued magnetic Schrödinger operators
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911706753531904 |
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| author | Addona, Davide Leone, Vincenzo Lorenzi, Luca Ouhabaz, El Maati Rhandi, Abdelaziz |
| author_facet | Addona, Davide Leone, Vincenzo Lorenzi, Luca Ouhabaz, El Maati Rhandi, Abdelaziz |
| contents | We consider vector-valued magnetic Schrödinger operators $-\bm Δ_{\bm a}+V$ with magnetic potential $\bm a \in L^2_{\mathrm{loc}}(\mathbb{R}^d;\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\mathrm{loc}}(\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\mathbb{R}^d;\mathbb{C}^m)$, $p\in[1,\infty)$ and the boundedness of the Riesz transforms $(\nabla - i\bm a)(-\bm Δ_{\bm a}+V)^{-\frac{1}{2}}$ and $V^α(-\bm Δ_{\bm a}+V)^{-α}$ on $L^p(\mathbb{R}^d;\mathbb{C}^m)$ for every $p \in (1,2]$ and every $α\in[0,1/p]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_19438 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal inequalities and Riesz transforms for vector-valued magnetic Schrödinger operators Addona, Davide Leone, Vincenzo Lorenzi, Luca Ouhabaz, El Maati Rhandi, Abdelaziz Analysis of PDEs 35J47, 47D08, 42B20, 42B37 We consider vector-valued magnetic Schrödinger operators $-\bm Δ_{\bm a}+V$ with magnetic potential $\bm a \in L^2_{\mathrm{loc}}(\mathbb{R}^d;\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\mathrm{loc}}(\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\mathbb{R}^d;\mathbb{C}^m)$, $p\in[1,\infty)$ and the boundedness of the Riesz transforms $(\nabla - i\bm a)(-\bm Δ_{\bm a}+V)^{-\frac{1}{2}}$ and $V^α(-\bm Δ_{\bm a}+V)^{-α}$ on $L^p(\mathbb{R}^d;\mathbb{C}^m)$ for every $p \in (1,2]$ and every $α\in[0,1/p]$. |
| title | Maximal inequalities and Riesz transforms for vector-valued magnetic Schrödinger operators |
| topic | Analysis of PDEs 35J47, 47D08, 42B20, 42B37 |
| url | https://arxiv.org/abs/2605.19438 |